I thought the answers that there can be no stimulated emission from excited gravitational states are correct, as there are no discrete bound states with the gravitational potential,but while exploring the suggestion by John whether one could make a free gravity laser in analogy to a free electron laser I found the following :
QUANTUM STATES OF NEUTRONS IN THE EARTH’S GRAVITATIONAL FIELD: STATE OF THE ART, APPLICATIONS, PERSPECTIVES
If one goes through the article, it is not a simple matter. A bound state of a neutron with the whole earth is not something one can build an inverted population with to create a laser. So the no should be qualified: beings who could experiment with ensembles of earths might be able to create inverted populations.
Now going to the gravitational analogue of a free electron laser I think we would have the same problem. The gravitational constant is very small, and it is necessary to use a neutral candidate so that the effect would not be masked by the electromagnetic changes, that one cannot see how an undulator with gravitational forces only could be attempted.
Schematic representation of an undulator, at the core of a free-electron laser.
The schema, because of the changes in acceleration might radiate coherent gravitational waves even as it is working with the charged electrons but due to the smallness of the gravitational constant these would be very weak , and , in my opinion , undetectable.
Of course all of the above with the assumption that gravity is quantized in the same way as the other three forces.